Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data.

This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.

Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation

This study presents a novel approach for simulating the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and the Haar wavelet collocation method. The proposed model considers various factors that affect virus transmission, while the Haar wavelet collocation method provides an efficient and accurate solution for the fractional derivatives used in the model. This study analyzes the impact of the Omicron variant and provides valuable insights into its transmission dynamics, which can inform public health policies and strategies that are aimed at controlling its spread. Additionally, this study's findings represent a significant step forward in understanding the COVID-19 pandemic and its evolving variants. The results of the simulation showcase the effectiveness of the proposed method and demonstrate its potential to advance the field of COVID-19 research. The COVID epidemic model is reformulated by using fractional derivatives in the Caputo sense. The existence and uniqueness of the proposed model are illustrated in the model, taking into account some results of fixed point theory. The stability analysis for the system is established by incorporating the Hyers–Ulam method. For numerical treatment and simulations, we apply the Haar wavelet collocation method. The parameter estimation for the recorded COVID-19 cases in Pakistan from 23 June 2022 to 23 August 2022 is presented.

Analysis of fractional COVID-19 epidemic model under Caputo operator.

The article deals with the analysis of the fractional COVID-19 epidemic model (FCEM) with a convex incidence rate. Keeping in view the fading memory and crossover behavior found in many biological phenomena, we study the coronavirus disease by using the noninteger Caputo derivative (CD). Under the Caputo operator (CO), existence and uniqueness for the solutions of the FCEM have been analyzed using fixed point theorems. We study all the basic properties and results including local and global stability. We show the global stability of disease-free equilibrium using the method of Castillo-Chavez, while for disease endemic, we use the method of geometrical approach. Sensitivity analysis is carried out to highlight the most sensitive parameters corresponding to basic reproduction number. Simulations are performed via first-order convergent numerical technique to determine how changes in parameters affect the dynamical behavior of the system.

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

SARS-CoV-2 and its variants have been investigated using a variety of mathematical models. In contrast to multi-strain models, SARS-CoV-2 models exhibit a memory effect that is often overlooked and more realistic. Atangana-Baleanu's fractional-order operator is discussed in this manuscript for the analysis of the transmission dynamics of SARS-CoV-2. We investigated the transmission mechanism of the SARS-CoV-2 virus using the non-local Atangana-Baleanu fractional-order approach taking into account the different phases of infection and transmission routes. Using conventional ordinary derivative operators, our first step will be to develop a model for the proposed study. As part of the extension, we will incorporate fractional order derivatives into the model where the used operator is the fractional order operator of order

Numerical solution of COVID-19 pandemic model via finite difference and meshless techniques.

In the present paper, a reaction-diffusion epidemic mathematical model is proposed for the analysis of the transmission mechanism of the novel coronavirus disease 2019 (COVID-19). The mathematical model contains six-time and space-dependent classes, namely; Susceptible, Exposed, Asymptomatically infected, Symptomatic infected, Quarantine, and Recovered or Removed (SEQIaIsR). The threshold number R0 is calculated by utilizing the next-generation matrix approach. Values of the parameters are estimated with the help of the least square curve fitting tools. In addition to the simple explicit procedure, the mathematical epidemiological model with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Stability analysis of the disease free and endemic equilibrium points of the model is investigated. Simulation results of the model with and without diffusion are presented in detail. A comparison of the obtained numerical results of both the models is performed in the absence of an exact solution. The correctness of the solution is verified through mutual comparison and partly, via theoretical analysis as well.

Numerical study of a nonlinear COVID-19 pandemic model by finite difference and meshless methods.

In this paper, a mathematical epidemiological model in the form of reaction diffusion is proposed for the transmission of the novel coronavirus (COVID-19). The next-generation method is utilized for calculating the threshold number R 0 while the least square curve fitting approach is used for estimating the parameter values. The mathematical epidemiological model without and with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Further, for the graphical solution of the non-linear model, we have applied a one-step explicit meshless procedure. We study the numerical simulation of the proposed model under the effects of diffusion. The stability analysis of the endemic equilibrium point is investigated. The obtained numerical results are compared mutually since the exact solutions are not available.

Fractional dynamics and stability analysis of COVID-19 pandemic model under the harmonic mean type incidence rate.

In this research, COVID-19 model is formulated by incorporating harmonic mean type incidence rate which is more realistic in average speed. Basic reproduction number, equilibrium points, and stability of the proposed model is established under certain conditions. Runge-Kutta fourth order approximation is used to solve the deterministic model. The model is then fractionalized by using Caputo-Fabrizio derivative and the existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Adam-Moulton scheme. Sensitivity analysis of the proposed deterministic model is studied to identify those parameters which are highly influential on basic reproduction number.

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function.

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana-Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik-Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan).

The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article. First, we formulate the model without control and study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Furthermore, we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host population. In order to do this, we use two control variables. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system. Taking into account the central manifold theory the bifurcation analysis is also incorporated. The numerical simulations are performed in order to show the feasibility of the control strategy and effectiveness of the theoretical results.